I can't find any authoritative ruling on what the bow limit is for Mirkwood Rangers, and how this factors into multiple faction armies, given that they come with a bow equipped.

I did find an army list in DoS which takes 66% bows, including 20 rangers and 10 palace guard, but I want to see it in writing how this is legal. I'm sure there must be some published errata that I'm missing. Can anybody help me out?

It is due to a special rule that is part of the Thranduil's Halls army list (and detailed therein - in the back of the There and Back Again book for the most up-to-date version). Rangers in warbands led by Tauriel, Legolas or Ranger Captains don't count towards the bow limit (i.e. they don't count as models with bow, nor as ones without when calculating the limit - simply ignore them completly and take a third of any other figures in the list). As such, you could have a force with 100% bows when led by those specific heroes, but Rangers in any other warband will count as normal.

As far as multiple factions are concerned, the bow limit is always calculated seperately per list. For example, you cannot take 12 High Elves with bows from the Rivendell list and ally them to 24 Khazad Guard from the Durin's Folk list; instead you could have 8 High Elves with Elven Blade, 4 with Elf bow, 16 Khazad Guard and 8 Dwarf Rangers with bow. Replacing the Elves in the example above with the new Mirkwoodians, you could have 12 Rangers (if led by Tauriel/Legolas/Ranger captain), or a normal warband with 4 Rangers and e.g. 8 Palace Guard.

Just found it. Thank you!

It seems that Legolas Greenleaf is specified, not Legolas Greenleaf, Prince of Mirkwood. That changes plans somewhat.

in the latest rule book that has come out it does state legolas green leaf prince of mirkwood.